基于自适应有限元的起伏地形MT二维正演模拟

本文利用自适应有限元方法模拟起伏地形对大地电磁数据的影响.其中非结构化网格的自动剖分采用基于后处理技术的后验误差方法(又称Z-Z方法)进行控制、加密;通过地堑、山脊、地垒、山谷四种模型讨论了起伏地形对大地电磁TE和TM两种极化模式的视电阻率和阻抗相位曲线的影响,其中仅取10 Hz(高频)和0.01 Hz(低频)两个频点进行分析.证实了复杂的地形条件对TM模式的影响要比对TE模式的影响大得多,在TM极化模式中,低频部分的视电阻率比高频部分的更容易受起伏地形影响,而在TE极化模式中,则刚好相反等重要结论,为实际工作提供了理论指导作用.     

Numerical modeling of 3-D terrain effect on MT field

Using the boundary element method, the numerical modeling problem of three-dimensional terrain effect on magnetotelluric (MT) field is solved. This modeling technique can be run on PC in the case of adopting special net division. The result of modeling test for 2-D terrain by this modeling technique is basically coincident with that by 2-D modeling technique, but there is a great difference between the results of 3-D and 2-D modeling for 3-D terrain. Project supported by the National Natural Science Foundation of China.     

Dynamic-stiffness matrix of soil by the boundary-element method: Embedded foundation

Green's influence functions are derived for a linearly distributed load acting on part of a layered elastic halfplane on a line which is inclined to the horizontal. Using these Green's functions as fundamental solutions in the boundary-element method, the dynamic-stiffness matrices of the unbounded soil with excavation, of the excavated part and of the free field are calculated. The indirect boundary-element method using distributed loads and no offset leads to more accurate results than the weighted-residual technique and the direct boundary-element method. At the natural frequencies of the undamped excavated part built-in along the structure-soil interface, the spring coefficients associated with the dynamic-stiffness matrices of the excavated part and of the free field will become infinite. If the dynamic-stiffness matrix of the soil with excavation is calculated as the difference of that of the free field and that of the excavated part, the difference of two large numbers will arise in the vicinity of these frequencies. A consistent discretization must then be used. In particular, the dynamic-stiffness matrix of the embedded part cannot be determined by the finite-element method in this case. A parametric study is performed for the dynamic-stiffness matrix of the free field for a rectangular foundation embedded in a halfplane and in a layer built-in at its base; the aspect ratio and the damping of the soil are varied.     

Dynamic-stiffness matrix of soil by the boundary-element method: Conceptual aspects

Starting from a weighted-residual formulation, the various boundary-element methods, i.e. the weighted-residual technique, the indirect boundary-element method and the direct boundary-element method, are systematically developed for the calculation of the dynamic-stiffness matrix of an embedded foundation. In all three methods, loads whose analytical response in the unbounded domain can be determined are introduced acting on the continuous soil towards the region to be excavated. In the weighted-residual technique and in the indirect boundary-element method, a weighting function is used; in the latter case, it is selected as the Green's function for the surface traction. In the direct boundary-element method, the surface traction along the structure-soil interface is interpolated. The same type of boundary matrices which have a clear physical interpretation are identified in the three formulations, each of which is illustrated with a simple static example. The indirect boundary-element method leads to the most accurate results. The guaranteed symmetry and the fact that the displacement arising from the applied loads can easily be calculated and compared to the prescribed displacement makes the indirect boundary-element method especially attractive for calculating the dynamic-stiffness matrix of the soil. Instead of calculating the dynamic-stiffness matrix of the embedded foundation with the boundary-element method, it can be determined as the difference of those of the regular free field and of the excavated part. The calculation of the former does not require the Green's function for the surface traction. The dynamic stiffness of the excavated part can be calculated by the finite-element method.     

起伏地形下各向异性的2D大地电磁无网格法数值模拟

作为一种基于节点的计算方法,无网格法具有构造高阶导数方便,自适应分析便利的优点,特别适合复杂地质构造的数值模拟.本文针对实际地球物理勘探中存在的起伏地形和各向异性的地电结构,提出用无网格法来模拟大地电磁响应,采用复合二次径向基函数构造了形函数,推导了大地电磁无网格法等价线性方程组,研究了系数矩阵的压缩存储方法以及大型稀疏复线性方程组快速求解算法,实现了起伏地形下各向异性的2D大地电磁高精度数值模拟.基于层状模型验证了算法的正确性,计算结果表明：无论是TM模式还是TE模式,计算相对误差均小于1%;通过对地垒和地堑模型的模拟,得出了起伏地形对视电阻率和相位的影响规律;对起伏地形下含有不同各向异性系数异常体的模型进行了数值模拟,为开展复杂地质结构的电磁场特征研究以及地形校正奠定了理论基础.随着计算科学的快速发展,无网格法必将成为新的高精度电磁场数值模拟方法.     

大地电磁二维自适应地形有限元正演模拟

复杂地形对大地电磁测深法(MT)的影响非常大。文中在吸收和修正前人工作基础上,提出了一种自适应地形四边形网格剖分、单元内电磁场双二次插值数值模拟方法,能更好地模拟出复杂地形和场值分布,并推导出复杂地形条件下有限元数值模拟算法、单元辅助场的计算和TM模式视电阻率的局部定义法。模型计算表明,该数值模拟方法计算速度快,有较高的计算精度,能很好地模拟MT复杂地形影响和异常体影响。     

Inversions for MT data in 2D symmetrical anisotropic media

Introduction Ready and Renkin (1971) were the first to make the research on anisotropy problems in magnetotellurics (MT). The progress in the research is not evident because it is more complex and difficult than isotropic problems. Now, the one-dimensional (1D) anisotropy problems in MT have been well solved, while for the two-dimensional (2D) cases, the numerical solutions have only been obtained for some particular conditions (Ready and Renkin, 1975). As to the three-dimensional (3D) ani…     

Influence of Elevation Data Source on 2D Hydraulic Modelling

The aim of this paper is to analyse the influence of the source of various elevation data on hydraulic modelling in open channels. In the research, digital terrain models from different datasets were evaluated and used in two-dimensional hydraulic models. The following aerial and satellite elevation data were used to create the representation of terrain–digital terrain model: airborne laser scanning, image matching, elevation data collected in the LPIS, EuroDEM, and ASTER GDEM. From the results of five 2D hydrodynamic models with different input elevation data, the maximum depth and flow velocity of water were derived and compared with the results of the most accurate ALS data. For such an analysis a statistical evaluation and differences between hydraulic modelling results were prepared. The presented research proved the importance of the quality of elevation data in hydraulic modelling and showed that only ALS and photogrammetric data can be the most reliable elevation data source in accurate 2D hydraulic modelling.     

Simulation of steady-state flow in three-dimensional fracture networks using the boundary-element method

An efficient method for simulating steady-state flow in three-dimensional fracture networks is formulated with the use of the boundary-element method. The host rock is considered to be impervious, and the fractures can be of any orientation and areal extent. The fractures are treated as surfaces where fluid movement is essentially two-dimensional. Fracture intersections are regarded as one-dimensional fluid conduits. Hence, the three-dimensional geometric characteristics of the fracture geometry is retained in solutions of coupled sets of one- and two-dimentional equations. Use of the boundary-element method to evaluate the fluid responses in the fractures precludes the need to internally discretize the areal extent of the fractures.     

面向目标自适应有限元法的带地形三维大地电磁各向异性正演模拟

传统三维大地电磁各向异性模拟均是基于规则六面体网格,计算精度有限且较难拟合复杂地质条件.本文采用面向目标自适应非结构矢量有限元法,对三维大地电磁各向异性介质进行模拟.首先从电场双旋度方程出发,利用伽辽金方法建立变分方程;然后利用电流密度连续性条件构建适合大地电磁各向异性问题的加权后验误差估计方法,实现面向目标的网格自适应正演;最后通过典型算例分析各向异性对网格自适应和大地电磁响应的影响特征以及各向异性的识别方法.本文算法能够高精度地拟合起伏地表和任意各向异性介质,适用于分析复杂地电条件大地电磁响应特征,为提高大地电磁资料解释水平提供了理论基础.

     

基于模型空间压缩的大地电磁三维反演研究

本文提出了一种基于模型空间压缩技术的大地电磁三维反演方法.该方法在传统大地电磁三维反演理论的基础上,通过小波变换将待反演的空间域模型参数映射到小波域进行反演,获得小波域更新模型后再通过小波逆变换得到空间域反演模型.由于小波变换具有压缩特性和多尺度分辨能力,本文反演方法可在一定程度上提高反演分辨率.为了提高反演效率,我们针对基于L1范数的模型约束求解不易收敛的反演问题,提出了一种基于模型粗糙度的简单有效的预条件处理技术.为验证本文算法的有效性,本文首先对经典的"棋盘"模型进行三维反演测试.反演结果表明本文算法的反演效率与传统方法相当,但对于深部异常体具有更好的分辨能力.最后,我们通过对实测数据反演进一步验证本文算法的有效性.     

凸起地形对地震动特性的影响

采用基于ABAQUS平台的显式有限元动力学分析方法,结合人工黏弹性边界理论,研究了局部凸起地形对地震动特性(包括反应谱、峰值加速度、峰值速度和峰值位移等)的影响,分析了台地宽度对地形放大效应的影响.结果表明:凸起地形平台段空间点地震动受地形效应影响较大,在零阻尼条件下,其谱比曲线呈双峰特点,.8—0.9s的中长周期段谱比达到一个较大值1.6,在0.08—0.09s的高频段谱比超过2.0,且最大值出现在平台中点;对于凸起地形斜坡段,在大部分周期点处,顶点的谱比高于其它斜坡点,而且在周期超过0.4s的频段,斜坡段观测点的谱比表现出较明显的规律性,即越靠近顶点的观测点,其谱比值越大;坡底段地表不同观测点的谱比基本在脚点与计算边界点(人工边界点)对应的谱比值之间变化,在不同的频段均表现出较明显的规律性.凸起地形平台段宽度对地震动高频成分的放大效应具有较大影响,但只局限在一定的宽度范围内,随着宽度的增大,其对地形放大效应的影响逐渐减弱. 此外,台地宽度的变化对地震动峰值加速度的放大效应有一定的影响,而对峰值速度、峰值位移的放大效应的影响则不明显.      

Modelling the effect of low soil temperatures on transpiration by Scots pine

For ecosystem modelling of the Boreal forest it is important to include processes associated with low soil temperature during spring‐early summer, as these affect the tree water uptake. The COUP model, a physically based SVAT model, was tested with 2 years of soil and snow physical measurements and sap flow measurements in a 70‐year‐old Scots pine stand in the boreal zone of northern Sweden. During the first year the extent and duration of soil frost was manipulated in the field. The model was successful in reproducing the timing of the soil warming after the snowmelt and frost thaw. A delayed soil warming, into the growing season, severely reduced the transpiration. We demonstrated the potential for considerable overestimation of transpiration by the model if the reduction of the trees' capacity to transpire due to low soil temperatures is not taken into account. We also demonstrated that the accumulated effect of aboveground conditions could be included when simulating the relationship between soil temperature and tree water uptake. This improved the estimated transpiration for the control plot and when soil warming was delayed into the growing season. The study illustrates the need of including antecedent conditions on root growth in the model in order to catch these effects on transpiration. The COUP model is a promising tool for predicting transpiration in high‐latitude stands. Copyright © 2006 John Wiley & Sons, Ltd.     

3D Modelling of the electromagnetic response of geophysical targets using the FDTD method1

A publicly available and maintained electromagnetic finite-difference time domain (FDTD) code has been applied to the forward modelling of the response of 1D, 2D and 3D geophysical targets to a vertical magnetic dipole excitation. The FDTD method is used to analyse target responses in the 1 MHz to 100MHz range, where either conduction or displacement currents may have the controlling role. The response of the geophysical target to the excitation is presented as changes in the magnetic field ellipticity. The results of the FDTD code compare favourably with previously published integral equation solutions of the response of 1D targets, and FDTD models calculated with different finite-difference cell sizes are compared to find the effect of model discretization on the solution. The discretization errors, calculated as absolute error in ellipticity, are presented for the different ground geometry models considered, and are, for the most part, below 10% of the integral equation solutions. Finally, the FDTD code is used to calculate the magnetic ellipticity response of a 2D survey and a 3D sounding of complicated geophysical targets. The response of these 2D and 3D targets are too complicated to be verified with integral equation solutions, but show the proper low- and high-frequency responses.     

多通道瞬变电磁法2D有限元模拟

多通道瞬变电磁法的反演工作是在大地脉冲响应的基础上进行的,因此本文用2D有限元正演来求取大地脉冲响应,实现多道瞬变电磁法的正演模拟研究.研究工作首先在有源大地电磁法2D有限元模拟的基础上进行,原有2D有限元法的频带相对于多通道瞬变电磁法的频带是窄频的,为此采用校正法将其扩展到所需的宽度,实现了频率域宽频带有源电磁勘探方法的正演模拟;然后通过频时变换变换到时间域,得到瞬变电磁法的阶跃响应;最后通过求取阶跃响应的时间导数,得到大地脉冲响应.针对多通道瞬变电磁方法的装置特点,用有一定埋深的顺层成矿模型分析了大地脉冲响应特征,发现对有一定埋深的顺层产出的矿脉模型来说,频率域电磁场结果以及时间域大地脉冲响应结果均需移除背景场才能突出异常体的存在,然而,在实际工作中,未知的背景场限制了其实用性.为此,本文利用多通道瞬变电磁方法数据量大的特点,提出用不同偏移距的等时曲线与等时断面来展示脉冲响应模拟结果,事实表明这两种展示方式可以清晰地分辨出矿体引起的异常,且能准确定位矿体的中心在地面的投影位置,从而说明多通道瞬变电磁方法相对于频率域有源电磁方法,对有一定埋深的顺层矿床有更高的分辨能力.

     

相邻地形对地震动特性的影响分析

基于采用透射人工边界的显式动力有限元方法,研究了相邻凸起地形对地震动反应谱特性的影响,分析了相邻凸起之间距离的变化对地形效应的影响。研究结果表明:1与单一凸起地形对地震动的放大效应相比,相邻地形的存在对地震动反应谱谱比曲线的形状影响不大,但对谱比的值具有较大影响,而且其影响程度的大小与地表观测点的位置有关;2相邻凸起地形的存在对凸起平台段中点地震动高频成分的放大效应影响较大,随着相邻凸起之间距离的增加,该影响逐渐减弱,多个相邻凸起构成的组合地形对地震动的放大效应逐渐接近单一凸起地形。     

Non-linear soil–structure interaction analysis based on the boundary-element method in time domain with application to embedded foundation

The various boundary-element methods, well established in the frequency domain, are developed in the time domain for a foundation embedded in a layered halfspace. They are the weighted-residual technique and the indirect boundary-element method, based on a weighted-residual equation, and the direct boundary-element method based on a reciprocity equation, both equations involving time and space. In the indirect approach, formulating the weighted-residual equation over the last time step only results in the truncated indirect boundary-element formulation which requires a reduced computational effort. In all cases, convolution integrals occur. The truncated indirect boundary-element method leads to a highly reliable algorithm, as is verified when a linear analysis in the time domain is compared to the corresponding one in the frequency domain. This boundary-element formulation, which is non-local in space and time, represents a rigorous generally applicable method taking into account a layered halfspace in a non-linear soil-structure interaction analysis. As an example, the non-linear soil-structure interaction analysis of a structure embedded in a halfspace with partial uplift of the basemat and separation of the side wall is investigated.     

大地电磁测深二维正演中辅助场的新算法

文中提出一种计算大地电磁二维正演辅助场的新方法。在主场满足线性插值基函数的前提下,通过构建二次插值基函数来提高辅助场计算中数值求导的精度。通过与线性插值函数法的计算结果进行对比,证明该算法在基本不增加计算量的同时可以大幅度提高大地电磁二维正演精度。文中还研究了网格对辅助场计算的影响,结果表明二次插值法较线性插值法对网格的要求更为宽松。此外还以均匀半空间模型为例讨论了地表网格纵向间距与模型之间的关系,这对正演计算中的网格设计有参考意义     

2D Optimized Electrode Arrays for Borehole Resistivity Tomography and CO2 Sequestration Modelling

Modern optimization approaches for electrode configurations can significantly improve the resolution of 2.5D resistivity imaging surveys. This study presents a brief review of the 2.5D optimization approach, particularly for borehole–borehole surveys with applications for mapping virtual CO₂ plumes sequestrated in deep saline reservoir formations. The applied algorithm searches for arrays that maximize the spatial resolution of the survey among the comprehensive dataset of best possible spatial resolution (i.e. least temporal resolution). A main goal of this study is to increase the temporal resolution of ERT borehole–borehole surveys by selecting optimized electrode configurations in order to minimise the required data acquisition time while sustaining a high spatial resolution. The optimized dataset starts with a base set and is iteratively increased based on the model resolution matrix (R ) until the required number of data points is achieved. Among four different optimization methods, the compare R (CR) method of the best resolution is applied to directly calculate R for each new array added to the optimized dataset. Small optimized datasets generated by this technique are only <5% of their comprehensive sets but of an average resolution ratio (R _r) of >0.95 (i.e. almost the same resolution). With increasing the size of the optimized dataset (during its generation), the algorithm progressively enhances R _r values in the central interwell region (of low sensitivities and low resolution) far higher than in the near borehole region (of high sensitivities). Also the inverted tomogram reliability increases by increasing the optimized data size. Briefly, the optimized arrays improve the resolution in the interwell region which is commonly low in borehole–borehole ERT studies. The inverted output model is evaluated quantitatively using the model difference relative to the input model. The results reflect the common smearing effects and artefacts of varying degrees that overpredict volumes, underpredict magnitudes and blur boundaries of the target anomalies. This input model is a synthetic resistivity model that was used to generate synthetic (forward solution) data used during the inversion. Applications on synthetic CO₂ models show that the mapping resolution for optimized datasets is better than that for other highly resolving arrays of the same number of data points. Problems of smeared boundaries and thin layers are less visible in the optimized array than in the other highly resolving arrays.     

基于三维正演的音频大地电磁阻抗相位不变量校正技术

复杂地形、地质条件的大地电磁数据解释容易出现假象,采用三维正演技术模拟地形和地表不均匀体的背景响应,对实测数据阻抗相位不变量进行校正,实现更准确的定性分析;对三维异常体模型的合成数据进行一维、二维多参数反演试算,以确定地形剧变区选择反演技术的最佳方案.合成数据的试反演结果显示一维反演水平切片假异常较多,二维反演能压制测向假异常,但不能压制走向的假异常,水平切片多出现测向条带.使用本文提出的阻抗相位不变量校正法扣除地形、地表背景响应,结合一维、二维反演,能使实际资料解释成果更加可靠.